Typical absorption type silencers or mufflers 10 shown in FIG. 1 (also known as dissipative silencers) include outer shell 12, and a porous pipe 14 connecting entry and exit pipes 14A and 14B for fluid communication of exhaust from an internal combustion engine. Sound absorbing material 18 is filled between the porous pipe 14 and the inner surface of the muffler chamber. Absorption silencers efficiently reduce acoustical energy in intermediate and high frequencies (typically above 200 Hz) by the sound absorbing characteristics of the sound absorbing material 18. The “broad band” absorption of acoustic energy is desired in automotive exhaust applications because the frequency of the acoustic energy produced by the engine will vary as the engine speed (RPM) changes and as the exhaust gas temperatures vary.
Another type of silencer is what is typically called a reflective silencer. In reflective silencers, elements are designed to reflect or generate sound waves that destructively interfere with sound waves emanating from the engine. One type of acoustic reflective element is commonly known as a Helmholtz resonator. A Helmholtz resonator is a chamber with an open throat. A volume of air located in the chamber and throat vibrates because of periodic compression of the air in the chamber. Helmholtz resonators may be attached to exhaust pipes of internal combustion engines as is shown in FIG. 3 to cancel noise caused by the firing of the pistons of the internal combustion engine (typically 30 to 400 Hz). FIG. 3 schematically illustrates a muffler 50 which includes a rigid outer shell 52, a Helmholtz resonator 54 which includes a throat portion 54a having an inner diameter DT, and a length LT, and a chamber portion 54b having an inner diameter DC, and a length LC.
Typically, the peak attenuation frequency of sound energy, i.e., the frequency at which the greatest transmission loss occurs, is a function of the volume of the chamber portion 54b of the Helmholtz resonator 54 and the throat portion inner diameter DT and length LT. For example, if the chamber volume increases and the throat portion inner diameter DT, and length LT remain the same, the peak attenuation frequency decreases, and if the chamber volume decreases, the peak attenuation frequency increases.
When the Helmholtz resonator 54 is attached as a side branch, as shown in FIG. 3, the side branch has both mass (inertia) and compliance. This acoustic system is called a Helmholtz resonator and behaves very much like a simple mass-spring damping system. The resonator has a throat with diameter DT and area Sb, an effective neck length of Leff=L+0.85DT, and a cavity volume V (a function of DC and LC). The cavity volume resonates at a frequency, and in the process of resonating, it interacts with energy. All of the energy absorbed by the resonator during one part of the acoustic cycle is returned to the pipe later in the cycle. The phase relationship is such that the energy is returned back towards the source—it does not get sent on down the duct. Since no energy is removed from the system, the real part of the branch impedance Rb=0. The imaginary part of the impedance may be expressed in terms of the compliance and inertia of the resonator, Xb=p(w Leff/Sb−c2/wV), so that the equation of the sound power transmission coefficient may be written as shown in equation (1).
                              T          Π                =                              ⌈                          1              +                              (                                                      c                    2                                                        4                    ⁢                                                                                            S                          2                                                ⁡                                                  (                                                                                    ω                              ⁢                                                                                                                          ⁢                                                                                                L                                  eff                                                                /                                                                  S                                  b                                                                                                                      -                                                                                                                            c                                  2                                                                /                                ω                                                            ⁢                                                                                                                          ⁢                              V                                                                                )                                                                    2                                                                      )                                      ⌉                                -            1                                              (        1        )            
The transmitted power is zero when w=w0 in Eq. (1), which is the resonance frequency of the resonator, at which all of the energy is reflected back towards the source. These filters decrease sound within a band around the resonance frequency, and pass all other frequencies. The narrow frequency range over which interference occurs is normally not a desired condition in an automobile exhaust since the frequency of the acoustic energy will vary as the engine speed (RPM) varies and as the temperature of the exhaust gases vary.